Eur. Phys. J. Plus (2024) 139: 556
https://doi.org/10.1140/epjp/s13360-024-05347-0

Regular Article

Alteration of cardiomyocyte apoptosis by nonlinear advection–diffusion dynamics of calcium and inositol 1,4,5-trisphosphate

Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath, 395007, Surat, Gujarat, India

^a nishasingh.maths@gmail.com

Received: 12 January 2024
Accepted: 2 June 2024
Published online: 26 June 2024

Abstract

Apoptosis is a self-governing process that involves the activation, expression, and regulation of a wide range of genes which activate programmed cell death to remove useless or abnormal cells in organisms to maintain the internal stability of the organisms. However, cancer cells are always resistant to apoptotic signals via a series of biochemical changes. One of the mechanisms of the killing of these cancerous cells is by increasing the level of intracellular calcium concentration $([{\text{Ca}}^{2+}])$. Evidence accumulated over the past decade indicates a pivotal role of inositol 1,4,5-trisphosphate receptor $({\text{IP}}_3\text{R})$-mediated calcium $({\text{Ca}}^{2+})$ release in the regulation of cytosolic and nuclear ${\text{Ca}}^{2+}$ signals. Altered expression of specific ${\text{Ca}}^{2+}$ channels and pumps is characterizing features of some cancers. In the present work, we have proposed a mathematical model to describe the mechanism of cardiomyocyte which focuses on the evaluation of the parameters which regulates cytosolic $[{\text{Ca}}^{2+}]$ as anticancer drugs and motivates to search for novel therapies to cure these malignancies by targeting complex ${\text{Ca}}^{2+}$ signaling process in cardiomyocytes. Our study suggests that the cytosolic $[{\text{Ca}}^{2+}]$ may be controlled by advection–diffusion of ${\text{Ca}}^{2+}$ with inositol 1,4,5-trisphosphate $({\text{IP}}_3)$ diffusion. It is found that Leak and source of calcium $(\sigma )$ act as intensifier supporting advection effect for cytosolic $[{\text{Ca}}^{2+}]$, whereas maximum production of ${\text{IP}}_3$$(V_{\text{Pd}})$ and diffusion coefficients $(D_{\text{c}}$ and $D_i)$ playing the role of down-toner to regulate cytosolic $[{\text{Ca}}^{2+}]$ level which offers the opportunity for a set of new drug targeted for treating cancer. We have also discussed the relevant approaches to overcome the increase in cancer cell due to altered apoptosis.